A Statistical Approach for Modeling the Aging Effects in ...netfficient-project.eu/.../2019/02/UNICA_A-Statistical-Approach-for-Modeling....pdfDistributed Energy Storage Systems (DESSs)

Received June 11, 2018, accepted July 9, 2018, date of publication July 25, 2018, date of current version August 20, 2018.

Digital Object Identifier 10.1109/ACCESS.2018.2859817

A Statistical Approach for Modeling the AgingEffects in Li-Ion Energy Storage SystemsMARIO MUREDDU 1, ANGELO FACCHINI2,3, AND ALFONSO DAMIANO1, (Member, IEEE)1Department of Electrical and Electronic Engineering, University of Cagliari, 09123 Cagliari, Italy2IMT School for Advanced Studies Lucca, 55100 Lucca, Italy3Italian National Research Council, Institute for Complex Systems, 00185 Roma, Italy

Corresponding author: Alfonso Damiano ([email protected])

This work was supported by the European Union’s Horizon 2020 Research and Innovation Program under Grant 646463. The work ofA. Facchini was supported in part by the EU projects OpenMaker under Grant 687941 and in part by the SoBigData under Grant 654024.

ABSTRACT This paper presents a novel approach for the technical and economic assessment of Li-ionbattery energy storage systems (BESS) in smart grids supported by renewable energy sources. The approachis based on the definition of a statistical battery degradation cost model (SBDCM), able to estimate theexpected costs related to BESS aging, according to the statistical properties of its expected cycling patterns.This new approach can improve the assessment of the economical sustainability of BESSs in this kind ofapplications, helping in this way the planning processes in electricity infrastructures in presence of highpenetration of intermittent renewable energy sources. The SBDCM proposed in this paper is a statisticalgeneralization of a battery degradation model presented in the literature. The proposed approach has beenvalidated numerically comparing the results with those of the deterministic model considering for the BESSa stochastic dataset of input signals. In order to test the usefulness of the proposed model in a real worldapplication, the proposed SBDCM has been applied to the evaluation of the economic benefit associated tothe development of distributed energy storage system scenarios in the Italian power system, aimed to provideancillary services for supporting electricity market.

INDEX TERMS Energy storage systems, energy storage management, statistical battery degradation model,renewable energy sources, ancillary services markets.

I. INTRODUCTIONThe increasing amount of Renewable Energy Sources (RESs)installed worldwide is introducing novel challenges in plan-ning and management of power systems. In particular,the fluctuating output of RESs sums up with the uncertaintyof load consumption, increasing the electricitymarket balanc-ing volumes and costs [1]. In this context, the Energy StorageSystems (ESSs) are foreseen as a possible solution in orderto reduce the workload of backup systems and improve theoverall stability of power systems [2], [3].

Despite of the results already obtained, nowadays the costand the efficiency of ESSs are still an open debate, sincemost of the approach proposed for economic evaluations arebased on a general lifetime estimation, and does not includea more precise aging evaluation for these type of systems.This is particularly true for Battery-based ESSs (BESSs),which aging properties can sensibly vary with the application,and are known to show a highly non-linear aging behavior.Nevertheless, some authors proposed different methods to

include a more accurate analysis of aging effects into the costfunction used for optimization usage of ESS, and particularlyBESSs, in power systems.

Among them, [4] highlighted this issue, proposing the useof a cycling based calculation of aging, finding how the BESSprofitability strongly depends on both the type of service forwhich the BESS is used for and the control method used forits management. Recently, a more advanced aging modelingof Li-ion BESSs has been proposed under the form of aBattery Degradation Model (BDM) [5]. This model is able toestimate the battery aging in a closed form considering boththe calendar aging, mainly due to the passage of time, and thecycling aging, due to the effective usage of the BESS. As animplementation of the proposed BDM, the implementation ofDistributed Energy Storage Systems (DESSs) for supportingthe Ancillary Services Markets (ASM) in power systemshas been considered and analyzed [5]. It points out howDESSs can effectively improve the reliability of power grids,reducing, at the same time, load curtailment. However, it also

421962169-3536 2018 IEEE. Translations and content mining are permitted for academic research only.

Personal use is also permitted, but republication/redistribution requires IEEE permission.See http://www.ieee.org/publications_standards/publications/rights/index.html for more information.

VOLUME 6, 2018

https://orcid.org/0000-0002-9908-9599

M. Mureddu et al.: Statistical Approach for Modeling the Aging Effects in Li-Ion Energy Storage Systems

underlines how different usage of BESSs due to different size,power to capacity ratio or control rules highly impacts onthe battery aging, which can in turn influence the economicprofitability of the process.

This is due to the complexity of the estimation of the agingcosts of the installed ESSs, which can significantly impacton the cumulative costs of energy services and depend inturn on the sequences of cycling and usage of the ESSs.Furthermore, the complexity of this task increases in caseof an high randomness of the charging/discharging cycles atwhich the BESS is subject to. In this case, the deterministicanalysis of the battery aging is impossible to achieve, since itsdegradation is highly dependent on the incoming random sig-nal. In order to overcome this critical issue a novel StatisticalBattery Degradation Model (SBDM) is proposed, aiming toevaluate the BESSs aging in highly stochastic environments,such as the ones involving an high RES penetration. Theproposed SBDM is therefore a statistical generalization of theBattery Degradation Model (BDM) proposed in [5].

The proposed SBDM relies on the assumption that, on along run, stochastic signals with the same time proper-ties (such as autocorrelation, expected value and amplitude)produce a similar aging effect on the same type of BESSs.This assumption has been tested numerically for Gaussianwhite noise and colored noise [6], [7]. In order to applythe SBDM in a real world application, an estimation of theeconomic impact of the implementation of a publicly ownedDistributed BESS (DESS) in the Italian Ancillary ServiceMarkets (ASM) has been performed. For this purpose, a Sta-tistical Battery Degradation Cost Model (SBDCM) has beenproposed, and further included in a more large Probabilis-tic Power Flow (PPF) framework. This approach allowedfor the statistical evaluation of the BESS aging in such acomplex environment. Furthermore, the aging effects havebeen described in terms of systemic costs by applying thecalculations proposed in subsec. IV-A. This finally allowedfor the evaluation of the global market costs in presence of aDESS, which include a detailed assessment of the expectedDESS aging costs.

The results confirm, in a more precise and cost effectiveway, the results shown in [4] and [5], which clearly state thatthe usage of BESS in ASM is economically advantageousonly under certain usage circumstances. Moreover, a sensi-tivity analysis shown the high dependence of the economicresult on the overnight costs and cumulative size of the DESS.

The paper is organized as follows: the proposed method-ology and the novel SBDM is firstly described in section II.Section III reports the procedure implemented for validatingthe SBDM. In Section IV the results of the application ofthe proposed model to the Italian ASM are presented anddiscussed. Finally, the conclusions are reported in section V.

II. THE STATISTICAL BATTERY DEGRADATIONCOST MODELThe estimation of the aging costs of BESSs is hard to achievefor applications including power inputs of stochastic nature.

This is due to the difficult estimation of the aging propertiesof batteries for both non-periodic usage schemes and ran-dom fluctuations. In order to overcome the first issue, [5]recently proposed a BDM able to estimate the aging of Li-ionBESSs in non-regular cycling use cases. Starting from thismodel, here is proposed a SBDM, based on the assumptionthat random signals with defined stochastic properties impactthe BESSs aging in a similar way. The SBDM is based onthe definition of the concept of average cycle, obtained as theintegral mean of the BDM proposed in [5], weighted withthe statistical distributions of the cycle properties.

These concepts are described in detail in the following sub-sections. In particular, subsection II-A briefly introduces theBDM proposed by Xu et al. [5], which will serve as a startingpoint for the following considerations. Then, subsection II-Bdescribes the here proposed SBDM, and defines an approachfor linking the statistic aging with a realistic cost estimationof the process.

A. DETERMINISTIC BATTERY DEGRADATION MODELThe deterministic BDM methodology defined in [5] is basedon (1), which relates the battery cycle life L with the batterydegradation function fd . The cycle life L is directly linkedwith the quantity D, the remaining capacity of the degradedBESS. In turn, fd depends on both cycle and calendar aging,which are the effects related to the battery cycling and thepassage of time, respectively. It also includes the effect of theinitial Solid Electrolyte Inter-phase (SEI) film formation bymeans of parameters αsei and βsei.

L = 1− αseie−βseifd − (1− αsei)e−fd (1)

The dependence of fd from the calendar aging function ft withthe cycle aging one fc can be found in (2), where N is thenumber of performed cycles.

fd (t, δ, σ, TC ) = ft (tuse, σ ,Tc)+N∑n

fc(δ, σ,Tc) (2)

More in detail, calendar aging function ft (tuse, σ ,Tc) ismodeled as dependent from average State Of Charge (SOC)σ and temperature Tc during usage, and from usage time tuse.The dependence from these parameters is reported in (3).In turn, the expression of St , Sσ and STC are described in (4),(5) and (6). The parameters kt , kσ , kT , σref and Tref have beenselected from [5].

ft (t, σ,TC ) = St (t) · Sσ (σ ) · STC (TC ) (3)

St (t) = kt t (4)

Sσ (σ ) = ekσ (σ−σref ) (5)

STC (TC ) = e−kT (TC−Tr ef )

TcTref (6)

Moreover, cycle aging function fc(δ, σ,Tc) depends onthe cycle Depth of Discharge (DoD) δ, the average SOC overthe cycle σ and the average temperature over the cycle Tc. Theexpression of fc(δ, σ,Tc) is given in (7). The expressions of

VOLUME 6, 2018 42197


Sδ , Sσ and STC are given by (8), (5) and (6). The parameterskδ1, kδ2 and kδ3 are obtained from [5].

fc(δ, σ,TC ) = Sδ(δ) · Sσ (σ ) · STC (TC ) (7)

Sδ(δ) = (kδ1δkδ2 + kδ3)−1 (8)

B. STATISTICAL GENERALIZATION OF THE BDMThe estimation of the degradation of BESSs in highly stochas-tic environments requires a statistical description of the bat-tery usage patterns, which does not fit with a deterministicformulation of the BDM proposed in [5]. This is due to therandomness of the signal in these cases. In fact, when theusage patterns of the BESS are stochastic, it is impossibleto know in advance its exact cycling. However, if the randomsignal shows specific statistical properties and is replicatedfor a long enough period, it is acceptable to assume that,on average, the cycling patterns will converge to a welldefined statistical distribution.

For this reason, the definition of the SBDM assumes astatistical description of the charge-discharge process. Thisdescription assumes that it is possible do estimate the cyclingstatistics of the BESS in terms of χ (tcyc, σ, δ, Tc), which isthe multivariate Probability Density Function of experiencinga cycle with a certain combination of tcyc, σ , δ and Tc. Thisdistribution χ depends on the particular application for whichthe BESS is used for. Once this quantity is known, it ispossible to estimate fd

cyc, which describes the degradation

function for a statistically representative cycle, which can beobtained by (9).

fdcyc=

∫ ∫ ∫ ∫χ (tcyc, σ, δ, Tc)

· fd (tcyc, σ, δ, Tc) · dσdδdTcdtcyc (9)

Once the quantity fdcyc

has been calculated, the expectedaging during a certain period T can be calculated by meansof (10) as a function of fd

cycand Ncyc, which is the number of

statistical representatives cycles observed in a time interval T .

f statd (T ) = Ncyc · fdcyc

(10)

Combining equations (1), (9) and (10), the battery life cyclecan be obtained from the proposed PPF cycles and describedin terms of L(N ), where N is the number of statistically rep-resentative cycles performed by each ESS. Given the averagecycle length 1tcyc, the quantity L(N ) assumes the form of atime dependent function Lt (t) as reported in (11).

Lt (t) = L(1tcyc · N ) (11)

Starting from this formulation, it is possible to identify theaging parameters of BESSs. It is common practice to consideran ESS as degraded when it reaches 80% of the originalcapacity C (L = 0.2). Using this information, and assumingthe quantity 1tcyc negligible with respect of the full batterylife time, the function Lt (t) can be considered continuous.In this way, the expected degradation time τ can be obtainedfrom (12).

τ = L−1t (0.2) (12)

This quantity is related with DESS depreciation costs by (13),where C inst are the total installation cost of the DESS, withC inst

= cinst · D0. Here D0 is the size of the installedBESS and cinst are its overnight costs per unity of capacity.Therefore, the average depreciation costs AD, during a giventime interval 1t , are obtained by performing (13).

AD =C inst

τD·1t (13)

Moreover, the maintenance cost M have been assumed to beproportional to the installation costs. This is achieved intro-ducing z which relates maintenance costs to the installationcosts, as reported in (14).

M = z · A (14)

III. NUMERICAL VALIDATION OF THE SBDMThis section aims to validate the assumptions behind theproposed SBDM, as defined in subsec. II-B. The first assump-tion A1 states that statistically equivalent BESS input signals,eventually filteredwith a well defined transfer function, causestatistically significant aging on equivalent BESS, providedthat the signal is applied for a long enough time interval.The second assumption A2 assumes that it is possible tostatistically define a ‘‘mean BESS cycle’’, which aging prop-erties are representative of the ones caused by the (eventuallyfiltered) input signal.

FIGURE 1. Validation process of the assumptions A1 and A2.

In order to validate the first assumption A1, consider thesimulation environment depicted in Fig. 1, left side. Theprocess starts with the generation of n independent and iden-tically distributed random time series Si(t), 0 < t < Tobtained from a certain statistical distribution 9, and withwell defined autocorrelation properties 4. Considering eachof these series Si(t) as the input profile of the same classof Li-ion BESS, eventually filtered with a transfer functionH (f (t)), it is possible to estimate the aging of the BESS attime T by applying (15), where B(g) represents the wholeBDM process described in II-A. If the set {DDi(T )} (standing

42198 VOLUME 6, 2018


TABLE 1. Means and standard deviations for the validation of A1assumption for WGN and AS signals.

for deterministic degradation) of the obtained aging outcomesshows a small enough statistical variability, the assumptioncan be considered valid. Here, the term small enough isdependent on the context and should be evaluated accordinglyto the needs of the application.

DDi(T ) = B(H (Si(t))), 0 < t < T (15)

In the following, the validity of this assumption is tested fortwo different sets of input signals, filtered with a transferfunction H (f (t)) corresponding with the so-called ‘‘dumbcontrol’’, described in the following. The considered inputsignals are defined by different 9 and 4 properties: a WhiteGaussian Noise (WGN), and an Autocorrelated Signal (AS)typical of medium sized power grids with high penetration ofRES [6], [7]. The WGN is a non-correlated Gaussian noise,obtained by independently generating random numbers froma Gaussian distribution [8]. On the other hand, in order to testthe assumption A1 with input signals representing a realisticapplication of a BESS, a set of AS series has been generatedby using an ARMA model [7]. The choice of the ARMAmodel for the sampling of power system output series hasbeen widely studied in literature [7], [9], and this model hasbeen shown to produce very good representation of this typeof signals. The ARMA parameters have been obtained byfitting a one-year long power time series, which is the output(at PCC) of the IEEE-69 nodes prototypical grid describedin [10] and [11]. The transfer function H , often called dumbcharging, is defined in (16). In the equation, Pavail(t) is theavailable BESS power output, as defined in (17) and (18),where EESS (t) is the energy stored in the BESS at time t , Pminand Pmax are the minimum andmaximum power output of theBESS.

Pin(t) =

{Pavail(t), if Pavail(t) ≤ Si(t)Si(t) otherwise

(16)

0.1 · D ≤ EESS (t) ≤ 0.9 · D (17)

Pmin ≤ Pavail(t) ≤ Pmax (18)

The numerical sampling of {DDi(T )} has been carried outfor both WGN and AS signal types with an average valueµ = 0 and standard deviation σ = 1, for a value of n = 500and a value of T = 10yr (520 weeks). The signals have beenapplied to a BESS of capacity C = 1 and a power to capacityratio of 1. All values are given in p.u. Results are shown intable 1, where DD(T ) and std(DD(T)) are the experimentalmean and standard deviation of the sample [6]. Also, the lattermeasure is considered as the sampling error. The outcomeshows a relative error of approximately 10−3, with the error

associated to the AS signal being around the double of theWGN one. This values can be considered acceptable for themain applications associated to this type of BESSs.

The assumption A2, states that the statistical description ofthe cycling patterns which arises from the function H (S(t))in terms of χ (tcyc, σ, δ, Tc) can be used for the definition ofa statistically representative cycle for the aging process. Theapplication of the SBDM in the form of (9) and (1) to thisrepresentative cycle can then be used for the estimation ofthe aging of the BESS. This represents a great advantage interms of assessment of the BESS life, since the definitionof χ (tcyc, σ, δ, Tc) becomes the only necessary input of themodel, which can be easily measured experimentally or esti-mated numerically. The flowchart of the validation processis shown in Fig. 1, right part. The outcome of the processis the value SL(t), representing the statistical aging curve ofthe BESS. In order to validate the results of this process,the resulting SL(t) has been calculated for both the WGNand the AS signals. In order to obtain a statistically rep-resentative χ (tcyc, σ, δ, Tc), the cycling patterns have beenevaluated numerically for a simulated time period of oneyear. Subsequently, the SL(t) curves have been comparedwith the results of the validation for the assumption A1. Thiscomparison in shown in Fig. 2. The result show that theresults of the SBDM fits with the variability of the numericalexperimental sampling in the case of the AS signal, whereasit tend to underestimate the battery aging by 0.1% in ten yearsin the case of the WGN signal. Anyway, this deviation is stillacceptable for the majority of the applications of this method.

FIGURE 2. The comparison between the statistical aging SL(t) and thenumerical sampling of aging for statistically equivalent signals. The plotshows the time evolution of the expected remaining capacity D(t) of theBESS in both cases, for both WGN and AS signals. Results show how thestatistical aging method provides a precise estimation of aging during theentire time frame, for both of tested signals.

IV. STATISTICAL COST EVALUATION OF THEIMPACT OF DESS IN THE ITALIAN ASMIn order to test the application of the newly proposed SBDMand SBDCM methods, it has been carried out an analysisof the economic sustainability of the usage of DESS in the

VOLUME 6, 2018 42199


Italian ASM. The usage of DESSs in ASM is of particu-lar interest because of the complex stochastic nature of thepower signals involved in these types of markets, especiallyin case of high penetration of intermittent RES. For thisreason, the installation of a public owned DESS oriented tothe filtering of RES and loads induced fluctuations can beuseful for the reduction of ASM prices, especially for whatconcerns the network balancing procedures. In order tomodelthis stochastic behavior of the network, the full balancingmarket procedure has been simulated numerically by meansof a PPF procedure coupled with the proposed SBDCM forthe estimation of the cumulative market costs, by followingthe process described in IV-A. Since it is difficult to includeBESS temperature factors in this type of analysis, the tem-perature of the considered BESS have been considered asconstant at tref = 25◦. The case study and simulation resultsconcerning the application of the proposed approach arereported in the following. Particularly, subsec. IV-A quicklyintroduces the balancing market simulation model proposedin [12]. This model has been used in combination withthe proposed SBDCM for the estimation of the economicimpact of Distributed ESSs in the balancing market of theItalian power system. The Subsec. IV-B introduces the Italianpower system, its related electricity market, and the DESSscenarios considered in the planning analysis. Subsequently,Subsec. IV-C reports the statistical results of the proposedmethodology regarding the DESS usage and the DESS cyclelife assessment. Finally, the results of the economic analysisare presented, discussed and compared with the canonicallifetime estimation methods in Subsec. IV-D.

A. APPLICATION OF THE SBDM TO THE ASSESSMENTOF ESS COSTS IN MARKET APPLICATIONSDifferent approaches have been proposed in technical liter-ature for the planning, the sizing and management of ESSsin power systems [3], [13]–[20]. In particular, the couplingbetween electricity markets and storage systems, making useof different techniques for mimicking the market, has beeninvestigated. This includes game theory-based approaches,time series reconstruction and risk-based algorithms will-ing to simulate the impact of ESSs on electricity markets.In recent years, the estimation of market volatility and costsin systems with high penetration of RES has been addressedwith Probabilistic Power Flow (PPF) procedures [21]–[24].The use of PPF procedures is necessary, since the randomnessof RES power production cannot bemodeledwith a determin-istic approach. As expected, the results of these approachesshow how, in general, an increase in the RES penetrationleads to an increased volatility in markets [24]. The use ofESS for the provision of ancillary services in power systemsis seen as a viable path to reduce the volatility of the associ-ated markets [10], [25], [26]. However, the lack of statisticalmodels for the assessment of battery degradation makes acorrect estimation of the Battery amortization costs difficultto achieve, possibly leading to an incorrect estimation of theglobal cost of the process.

In order to test a real world application of the proposedSBDM, it has been performed an investigation of the eco-nomic sustainability of a DESS for the provision of ancillaryservices in power systems. This has been achieved by inte-grating the SBDM with a Probabilistic Power Flow (PPF)procedure. Results have been used to identify the bestDESS configurations under different price scenarios. Finally,the best solutions for each scenario have been analyzed tounderstand the economic sustainability of DESSs by consid-ering different overnight costs.

The overall procedure consists in the evaluation of theresults of a PPF performed on the system under varying con-ditions, given by different combinations of DESS sizesD andovernight costs cinst . A schematic summary of the procedureis given in Fig. 3.

FIGURE 3. The flowchart of the proposed methodology.

The PPF procedure is necessary since the balancing pro-cess in power systems is intrinsically random, due to the inter-mittent nature of power demand and RES generation. In thispaper, the proposed PPF procedure resorts to the stochasticsampling procedure proposed in [12]. This procedure con-sisted in the sampling of R possible market configurationsper each combination of D and C inst . Each sample obtainedby the procedure is in fact the merit-order based OPF of thespecific realization, obtained by stochastically perturbing theinitial condition. As outcome of each of the samplings, it hasbeen possible to obtain both a series of total market costs anda series of time evolutions of the SOC of the ESSs composingthe DESS, which allowed in turn the calculation of the agingcosts associated to the usage of DESSs in the consideredscenario. All these costs have then been aggregated with theDESS maintenance costs, allowing for the estimation of theglobal system costs in all the simulated scenarios.

The market costs of DESSs are described by means ofa statistical distribution representing the market cumulativecost CCD. This cumulative cost is related to: the daily market

42200 VOLUME 6, 2018


costs CD; the depreciation costs of the entire DESS AD(cinst );its maintenance costs MD(cinst ); and the costs of its asso-ciated losses ID. In turn, all these quantities depend on D,the planned DESS capacity, and are evaluated considering thetime period 1t according to (13). In particular, the distribu-tion CCD can be calculated as reported in (19).

CCD = CD + AD +MD + ID (19)

In general, CD,AD,MD and ID depend on the DESS config-uration. Particularly, CD and ID are obtained directly fromthe PPF procedure, and generally vary for varying DESScapacities. The estimation of AD and MD can be determinedby means of the proposed SBDCM.

The estimation ofCCD allows for the identification of otherimportant key performance indexes of the proposed scenario:the DESS Total Repay Time (TRT) τDTRT and the Total RepayRatio (TRR) τDTRR. In particular, since the expected effectof DESS is the reduction of the balancing market costs,the economic improvement of GD can be determined bymeans of (20), where Kref are the market costs in a certainreference market configuration.

GD = Kref − CD − ID (20)

Given the overnight costs C inst , the system’s TRT and TRRare calculated by means of (21) and (22) respectively.

τDTRT =(1+ z)C inst (D, cinst )

GD(21)

τDTRR =τDTRT

τD(22)

B. CASE STUDY: APPLICATION TO THEITALIAN POWER SYSTEMThe proposed methodology has been applied referring to thebalancing phase of the ASM of the Italian power system.The tested DESS have been spatially distributed consideringas planning criteria the expected power variability inducedby RES and load of each node. The system configurationhas been obtained from two main datasets. The first one,is extracted from the public documentation provided by theItalian Transmission System Operator (TSO) TERNA on itswebsite which gives the characteristics of the power system.It includes the location of each 220 and 380 kV substa-tions and the distribution of transmission lines with theirelectrical characteristics. The location of conventional gen-erators with both their power rates and ramp limits is alsodetailed. Moreover, it includes a description of the systemmarket zones. The second dataset is provided by the Ital-ian market supervisor (GME) on its website. It reports thedetailed time evolution of production and consumption foreach 15 minutes of reference days. The RES production hasbeen estimated referring to the procedure described in [12],using the original datasets regarding the wind and photo-voltaic local production published on its website by the Italianauthority for RES, the GSE. The resulting structure of theItalian power system is reported in Fig.4. The red circles

FIGURE 4. Geographical representation of the Italian power systememployed as case of study. The red circles are the generation nodeswhere the balancing market transaction are allowed, while blue edgesare the transmission lines.

are the generation nodes where the balancing market trans-action are allowed, while blue edges are the transmissionlines. In this paper, the methodology for the economic assess-ment described in IV-A has been applied considering dif-ferent planning scenarios characterized by DESS cumulativecapacities of D = 1, 2, . . . , 10 GWh respectively. The PPFprocedure consisted in the sequential sampling of 1000 fullreference days. In turn, each day consisted in evaluating thetime evolution of 96 time intervals, representing the systemprogression in 15 minutes steps.

C. BATTERY USAGE AND DEGRADATION RESULTSThe simulation results are presented in Figs. 5, 6, 7 and 8.In particular, 5 shows a representation of the bivariate dis-tribution χ (δ, σ ), for a value of D = 1 GWh. Fig. 6 showsthe statistical distribution of cycles time length χtcyc (tcyc) pereach tested value of D. Furthermore, Fig 7 shows the cyclelife curve D = 1 − Lt (t) of the DESS, where the red dottedline refers to a remaining cumulative capacity ratio of 80%,at which the batteries of DESS can be considered degraded.Finally, Fig. 8 reports the statistical distribution of DoDsχδ(δ), for all the tested values of the DESS capacities D.Fig. 5 shows the obtained distributionχ in terms of δ and σ ,

which show an high probability to experience cycles withδ ≈ 0.1, being them at low or high average σ . The results ofFig. 6 highlight how the ESS cycling periods are narrowly dis-tributed around an average value tcyc characterized by a valueof 45 minutes which is not affected by the variation of the

VOLUME 6, 2018 42201


FIGURE 5. The numerically obtained multivariate Probability DensityFunction of χ(δ, σ ), for a value of D = 1 GWh. In general, the χ(δ, σ )shows a decreasing trend for increasing δ and σ , showing the presence ofan high number of low DoD cycles.

FIGURE 6. Statistical distribution of the time length of cycles, perdifferent values of D (cumulative capacity). Though very noisy, the mostexpected time length is around 45 minutes for every consideredvalue of D.

cumulative capacity D of DESS. Figs. 5 and 6, together, pro-vide a graphical representation of χ (tcyc, σ, δ, Tc) used in (9)for the calculation of the aging of the statistical representa-tive cycle fd

cyc(since Tc is considered constant during the

entire process). By applying (1), (9) and (10) to the obtainedχ (tcyc, σ, δ, Tc) it has been possible to assess the DESS lifecycle for the case of study considering different values ofcumulative capacitiesD. These findings are reported in Fig. 7,and show how bigger DESS sizes are related to higher batterylife. This is mainly due to the different cycling patterns ofthe tested DESS, as shown in the χδ(δ) distribution reportedin Fig. 8, for all the tested values ofD. Looking at this Figure,it is clear how the higher is D, the smaller is the averagecycling DoD performed by the DESS, increasing in this waythe expected DESS life cycle.

FIGURE 7. Degradation curves per different values of D (cumulativecapacity). Each curve shows the time evolution of D(t), the remainingcapacity after time t . In general, battery expected lifetime increases withincreasing installed capacity, ranging between 3 and 5.5 yrs.

FIGURE 8. Estimated statistical distribution of the cycling Depth ofDischarge δ per different values of D (cumulative capacity).

The previously given findings allow the identification ofτD, which increases monotonically with D ranging between1050 and 2000 days, i.e. 3 and 5.5 years. Considering thevalue of tcyc = 45 mins, the number of statistically represen-tative cycles, before degradation of ESSs occur, correspondto values ranging between 35000 and 60000. Such relevantnumber is explained by the frequent cycling characterizedby small DoD, which is related to the intermittence of theancillary service in the balancing market at which the ESSsare devoted to. The larger τD for increasing values of D ismainly due to the different shapes of the χδ(δ,D). As reportedin Fig. 8, high values of D show an increased probabilityof performing low DoD cycles, which in turn impact lesson the battery degradation. Furthermore, in Fig. 9 the pdistribution for the analyzed case study, which reports thedelivered power ratio for different values of D, is presented.

42202 VOLUME 6, 2018


FIGURE 9. Simulation results of the proposed methodology achieved forthe Italian power system oriented to the stochastic analysis of the usagepatterns of the DESS. Probability to provide a power ratio p, for each ESSof the system. Results are shown for DESS cumulative capacities ofD = 2,4,6,8 and 10 GWh respectively.

It refers to DESSs cumulative capacities of D = 2, 4, 6, 8and 10 GWh respectively. Results show how these distribu-tions are bimodal, revealing one peak around low values of pand one peak around 100% of the available power. The prob-ability of observing p = 100% strongly depends on the DESScapacityD. In particular, a DESSwithD = 10 GWhworks atfull power with a probability of 10%. This value increases fordecreasing installed capacity, and for D = 4 GWh the DESSworks at power rate higher than > 50% of rating power formore than 50% of the time. The reduced power usage of theDESS in the balancing phase can translate in free resources,which can be used for providing further ancillary services tothe system.

D. COSTS ESTIMATIONThe information regarding the battery life cycle obtained bythe PPF+SBDCM methodology in the Italian power systemhas been used to identify the average daily market cumulativecostsCCD for different cumulative capacitiesD. These valuesrepresent the combined cost of the balancing market of thesystem, summed with the battery depreciation and operativecosts. In order to compare these results with the currentconfiguration, the results include the CCref , which are thebalancing market costs for a cumulative capacity of DESSD equal to zero. If the decrease in daily market costs due tothe presence of the DESS is larger than its daily deprecia-tion and operative costs, then CCD < CCref . In this case,the installation of DESS is economically advantageous withrespect to the current configuration. Since the depreciationcosts AD of the DESS depends on its overnight costs perunit of capacity, the CCD has been evaluated for the differentvalues of cinst ranging between 200 and 800 Euros/kWh. Theobtained results for this case study are shown in Fig. 10.

Particularly, the cumulative costs curves show a non-monotonic behavior, with a global minimum dependent

FIGURE 10. Simulation results regarding the daily cumulative balancingmarket cost of the analyzed case study versus the cumulative capacity ofDESS for different values of specific cost of battery capacity c inst .

FIGURE 11. Comparison between the cumulative market costs calculatedwith aging costs obtained with both SBDM (continuous line) and a fixed5 yr lifetime (dashed line) for different values of specific cost of batterycapacity c inst .

on cinst . This minimum has been found to be smaller thanCCref for every value of cinst in the considered case study.The relative decrease in cumulative costs ranges from about10% for cinst = 800 Euro/kWh, to a value of 30% for acinst = 200 Euro/kWh. Moreover, the proposed methodol-ogy allows for the identification of the storage capacity Dminimizing the daily cumulative cost of the balancing marketfor different values of cinst . As expected, the outcome of theanalysis sensibly varies with cinst . In particular, the analysiswith cinst = 800 Euro/kWh shows a minimum cost regionaround of a cumulative capacity of 1 GWh, whereas a value ofcinst = 200 Euro/kWh shows an range of cumulative capacitybetween between 2 and 5GWh. This result highlights how theinstallation of a DESS for balancing purposes is economicallyprofitable in the case study. Finally, Table 3 shows the valuesof τDTRT and τDTRR for different combinations of D and cinst

in the case of study. These quantities represent, respectively,

VOLUME 6, 2018 42203


TABLE 2. Values of τDTRT and τD

TRR for different combinations of D and c inst in the analyzed case of study. The green cells highlight the economicallysustainable results, the red cells highlight the non-economically sustainable ones.

TABLE 3. List of acronyms used in the paper.

the payback time of the DESS for different values of D, andthe ratio between the payback time and the DESS degradationtime. The DESS can be fully payed back only if τDTRR < 1.As expected, τDTRT and τDTRR clearly increase with growing Dand cinst . Results confirm how each value of cinst has a rangeof installed storage D which makes DESSs economicallysustainable, just by providing ancillary services to balancingmarkets. The analysis of the results represents the expectedfeedback in the planning process of DESS.Moreover, as high-lighted by Fig.9 for this particular case study, the applica-tion of DESS in the balancing market leaves a significantprobability to experience free DESS power capacity, usefulto provide further ancillary services.

Finally, the obtained results have been compared with anestimation of the market cumulative costs in which the DESSamortization costs have been assessed by considering a fixedlifetime estimation of 5 yrs. The comparison shows how thisresults tends to underestimate the global costs for small DESS

sizes, and to overestimate them for big DESS sizes. This isdue to the fact that smaller BESSs tend to perform more highDoD cycles, which reduces their expected lifetime. If thiseffect is not correctly characterized, their amortization costsare underestimated, leading to a non correct estimation of theglobal costs of the process. This in turn can lead to a noncorrect planning procedure.

V. CONCLUSIONThe introduction of a statistical-based assessment of theLi-Ion BESS degradation allows for the estimation of theamortization costs of this type of batteries for use casesin highly stochastic operating conditions. The model, oncevalidated on two toy-model test cases, has been applied forthe assessment of the electric and economic impacts of dif-ferent DESS planning scenarios on the Italian market-basedpower system, by also including the battery aging effects.In particular, the results of the case study put in evidencethe existence of an economically sustainable configurationof DESS, with optimal size dependent on its overnight costsand ranging between 1 and 5 GWh. Moreover, the powerusage statistics of the DESS during the provision of ancillaryservices in balancing markets show a significant availabilityof spare resources, allowing the provision of further ancillaryservice in the balancing market. The obtained results makethe proposed methodology suitable for further investigationrelated to economic evaluation of additional services that canbe provided by Li-ion ESS, especially for use cases involvingthe random usage of this devices.

ACKNOWLEDGMENTThis work was developed within the project NETfficient,‘‘Energy and Economic Efficiency for Today’s Smart Com-munities through Integrated Multi Storage Technologies’’.

REFERENCES[1] M. Hildmann and A. Ulbig, ‘‘Empirical analysis of the merit-order effect

and the missing money problem in power markets with high RES shares,’’IEEE Trans. Power Syst., vol. 30, no. 3, pp. 1560–1570, May 2015.

42204 VOLUME 6, 2018


[2] S. Vazquez, S. M. Lukic, E. Galvan, L. G. Franquelo, and J. M. Carrasco,‘‘Energy storage systems for transport and grid applications,’’ IEEE Trans.Ind. Electron., vol. 57, no. 12, pp. 3881–3895, Dec. 2010.

[3] A. Saez-de-Ibarra et al., ‘‘Management strategy for market participationof photovoltaic power plants including storage systems,’’ IEEE Trans. Ind.Appl., vol. 52, no. 5, pp. 4292–4303, Sep. 2016.

[4] Y. Yang, H. Li, A. Aichhorn, J. Zheng, and M. Greenleaf, ‘‘Sizingstrategy of distributed battery storage system with high penetration ofphotovoltaic for voltage regulation and peak load shaving,’’ IEEE Trans.Smart Grid, vol. 5, no. 2, pp. 982–991, Mar. 2014. [Online]. Available:http://ieeexplore.ieee.org/document/6609116/

[5] B. Xu, A. Oudalov, A. Ulbig, G. Andersson, and D. Kirschen, ‘‘Modelingof lithium-ion battery degradation for cell life assessment,’’ IEEE Trans.Smart Grid, vol. 9, no. 2, pp. 1131–1140, Mar. 2016.

[6] D. Chandler, Introduction to Modern Statistical Mechanics. London, U.K.:Oxford Univ. Press, 1987.

[7] S.-J. Huang, S. Member, and K.-R. Shih, ‘‘Short-term load forecasting viaARMAmodel identification including non-Gaussian,’’ IEEE Trans. PowerSyst., vol. 18, no. 2, pp. 673–679, May 2003.

[8] C. S. Wallace, ‘‘Fast pseudorandom generators for normal and exponentialvariates,’’ ACM Trans. Math. Softw., vol. 22, no. 1, pp. 119–127,1996. [Online]. Available: http://portal.acm.org/citation.cfm?doid=225545.225554

[9] S. Paoletti, M. Casini, A. Giannitrapani, A. Facchini, A. Garulli, andA. Vicino, ‘‘Load forecasting for active distribution networks,’’ in Proc.2nd IEEE PES Int. Conf. Exhib. Innov. Smart Grid Technol., Dec. 2011,pp. 1–6.

[10] S. Korjani, M. Mureddu, A. Facchini, and A. Damiano, ‘‘Aging costoptimization for planning and management of energy storage systems,’’Energies, vol. 10, no. 11, pp. 1–17, 2017.

[11] A. R. Malekpour and A. Pahwa, ‘‘Radial test feeder includingprimary and secondary distribution network,’’ in Proc. North Amer.Power Symp. (NAPS), Oct. 2015, pp. 1–9. [Online]. Available:http://ieeexplore.ieee.org/document/7335222/

[12] M. Mureddu, G. Caldarelli, A. Chessa, A. Scala, and A. Damiano, ‘‘Greenpower grids: How energy from renewable sources affects networks andmarkets,’’ PLoS ONE, vol. 10, no. 9, p. e0135312, Sep. 2015.

[13] A. Damiano, G. Gatto, I. Marongiu, M. Porru, and A. Serpi, ‘‘Real-timecontrol strategy of energy storage systems for renewable energy sourcesexploitation,’’ IEEE Trans. Sustain. Energy, vol. 5, no. 2, pp. 567–576,Apr. 2014.

[14] H. Beltran, E. Bilbao, E. Belenguer, I. Etxeberria-Otadui, and P. Rodriguez,‘‘Evaluation of storage energy requirements for constant production in PVpower plants,’’ IEEE Trans. Ind. Electron., vol. 60, no. 3, pp. 1225–1234,Mar. 2013.

[15] A. Mohd, E. Ortjohann, A. Schmelter, N. Hamsic, and D. Morton, ‘‘Chal-lenges in integrating distributed Energy storage systems into future smartgrid,’’ in Proc. IEEE Int. Symp. Ind. Electron., Jun. 2008, pp. 1627–1632.

[16] M. Ghofrani, A. Arabali, M. Etezadi-Amoli, and M. S. Fadali, ‘‘A frame-work for optimal placement of energy storage units within a power systemwith high wind penetration,’’ IEEE Trans. Sustain. Energy, vol. 4, no. 2,pp. 434–442, Apr. 2013.

[17] P. Zou, Q. Chen, Q. Xia, G. He, and C. Kang, ‘‘Evaluating the contributionof energy storages to support large-scale renewable generation in jointenergy and ancillary service markets,’’ IEEE Trans. Sustain. Energy, vol. 7,no. 2, pp. 808–818, Apr. 2016.

[18] B. Lian, A. Sims, D. Yu, C. Wang, and R. W. Dunn, ‘‘Optimizing LiFePO4battery energy storage systems for frequency response in the UK system,’’IEEE Trans. Sustain. Energy, vol. 8, no. 1, pp. 385–394, Jan. 2017.

[19] H. Pandžić, Y. Wang, T. Qiu, Y. Dvorkin, and D. S. Kirschen, ‘‘Near-optimal method for siting and sizing of distributed storage in a transmis-sion network,’’ IEEE Trans. Power Syst., vol. 30, no. 5, pp. 2288–2300,Sep. 2015.

[20] R. Hemmati, H. Saboori, and S. Saboori, ‘‘Stochastic risk-averse coor-dinated scheduling of grid integrated energy storage units in transmis-sion constrained wind-thermal systems within a conditional value-at-riskframework,’’ Energy, vol. 113, pp. 762–775, Oct. 2016.

[21] X. Wang, Y. Gong, and C. Jiang, ‘‘Regional carbon emission managementbased on probabilistic power flow with correlated stochastic variables,’’IEEE Trans. Power Syst., vol. 30, no. 2, pp. 1094–1103, Mar. 2015.

[22] M. Hajian, W. D. Rosehart, and H. Zareipour, ‘‘Probabilistic power flowby Monte Carlo simulation with Latin supercube sampling,’’ IEEE Trans.Power Syst., vol. 28, no. 2, pp. 1550–1559, May 2013.

[23] M. Aien, M. Fotuhi-Firuzabad, M. Rashidinejad, and M. G. Khajeh,‘‘Probabilistic power flow of correlated hybrid wind-photovoltaic powersystems,’’ IET Renew. Power Gener., vol. 8, no. 6, pp. 649–658, 2014.

[24] M. Mureddu and H. Meyer-Ortmanns, ‘‘Extreme prices in electricity bal-ancing markets from an approach of statistical physics,’’ Physica A, Stat.Mech. Appl., vol. 490, pp. 1324–1334, Jan. 2018. [Online]. Available:http://arxiv.org/abs/1612.05525

[25] H. H. Abdeltawab and Y. A.-R. I. Mohamed, ‘‘Market-oriented energymanagement of a hybrid wind-battery energy storage system via modelpredictive control with constraint optimizer,’’ IEEE Trans. Ind. Elec-tron., vol. 62, no. 11, pp. 6658–6670, Nov. 2015. [Online]. Available:http://ieeexplore.ieee.org/document/7110555/

[26] I. Momber, A. Siddiqui, T. G. S. Román, and L. Söder, ‘‘Risk aversescheduling by a PEV aggregator under uncertainty,’’ IEEE Trans. PowerSyst., vol. 30, no. 2, pp. 882–891, Mar. 2015.

MARIO MUREDDU received the Ph.D. degree inphysics from the University of Cagliari in 2015.From 2015 to 2016, he held a post-doctoral posi-tion for two years at Jacobs University Bremen.He has been holding a post-doctoral position atthe University of Cagliari since 2017. His researchinterests span the application of complex systems,artificial intelligence, and blockchain to sustain-able energy applications. In particular, he focusedonmodeling the role of energy storage systems and

energy markets during the renewable energy transition, and in the modelingand planning of electric mobility on local and regional scale.

ANGELO FACCHINI received the degree intelecommunications engineering and the Ph.D.degree in physical chemistry. From 2003 to 2009,he visited as a Guest Scientist at the Max PlanckInstitute for the Physics of Complex Systems,Dresden. He is currently an Assistant Professorwith the IMT School for Advanced Studies Luccaand anAssociate Scientist with the Italian NationalResearch Council, Institute for Complex Systems.His research interests are in the field of data sci-

ence, complex systems, and sustainability science. In the field of complexsystems, his research focuses on nonlinear dynamics, stochastic processes,statistical physics, and complex networks. In the field of sustainabilityscience, he develops his research on urban development, urban metabolism,megacities, and in general on the relation between energy, water, and urban-ization, including energy and water infrastructures. On the above-mentionedtopics, he has published over 40 papers in international journals, amongthese PNAS, Nature Energy, Scientific Reports, Physical Review E, AppliedEnergy, and Energy.

VOLUME 6, 2018 42205


ALFONSO DAMIANO (M’12) was born inCagliari, Italy, in 1966. He received theGraduationdegree in electrical engineering from the Univer-sity of Cagliari, Cagliari, in 1992.

In 1994, he joined the Department of Elec-trical and Electronic Engineering, University ofCagliari, as an Assistant Professor. Since 2001,he has been an Associate Professor of electri-cal energy management and electrical machines.Since 2012, he has been a Visiting Professor with

the Institute for Advanced Studies of Lucca, Lucca, Italy. He is a Sci-entific Coordinator of the Sardinian Regional Renewable Energy Labora-tory, Cagliari. In 2013, he was a main Scientific Advisor of Project SmartCity, A Labeled Municipalities. Since 2013, he has been involved, as amain Scientific Advisor in the development and implementation of two

experimental microgrids based on novel energy storage management sys-tems, the project is supported by the European Community. He has authored140 papers published in international conference proceedings and journals.His current research interests include electrical drives, energy management,and energy storage systems, especially regarding electric vehicle and renew-able energy system applications.

Prof. Damiano is a member of the Industrial Application Society,Industrial Electronic Society, the Vehicular Technology Society, and thePower Engineering Society. He received the Sustainable Energy Europeand Managenergy Award from the European Commission in 2014.He also received the Second Prize Paper Award from the Power Elec-tronics Technical Committee of the IEEE Industrial Electronics Soci-ety at the 39th Annual Conference of the IEEE Industrial ElectronicsSociety.

42206 VOLUME 6, 2018

Documents

A Statistical Approach for Modeling the Aging Effects in ...netfficient-project.eu/.../2019/02/UNICA_A-Statistical-Approach-for-Modeling....pdfDistributed Energy Storage Systems (DESSs)